calculate the mass defect and the nuclear binding energy of nitrogen - 14. the mass of a proton is 1.00728…
calculate the mass defect and the nuclear binding energy of nitrogen - 14. the mass of a proton is 1.00728 amu, and the mass of a neutron is 1.00866 amu. the mass of a nitrogen - 14 atom is 14.00307 amu. the mass defect of nitrogen - 14 is amu. round to the 5th decimal place. the nuclear binding energy of one nitrogen - 14 atom is x 10^a j. round to 3 significant digits. a: done
Answer
Explanation:
Step1: Determine number of protons and neutrons
Nitrogen - 14 has 7 protons and 7 neutrons.
Step2: Calculate the sum of the masses of protons and neutrons
The mass of 7 protons is $7\times1.00728\ amu = 7.05096\ amu$. The mass of 7 neutrons is $7\times1.00866\ amu=7.06062\ amu$. The sum of the masses of protons and neutrons is $7.05096 + 7.06062=14.11158\ amu$.
Step3: Calculate the mass - defect
The mass - defect $\Delta m$ is the difference between the sum of the masses of protons and neutrons and the actual mass of the atom. $\Delta m=14.11158 - 14.00307=0.10851\ amu$.
Step4: Convert mass - defect to kg
We know that $1\ amu = 1.66054\times10^{- 27}\ kg$. So, $\Delta m = 0.10851\times1.66054\times10^{-27}\ kg=1.8027\times10^{-28}\ kg$.
Step5: Calculate the nuclear binding energy
Using Einstein's mass - energy equivalence formula $E = mc^{2}$, where $c = 3\times10^{8}\ m/s$. $E=(1.8027\times10^{-28}\ kg)\times(3\times10^{8}\ m/s)^{2}$ $E = 1.62243\times10^{-11}\ J\approx1.62\times10^{-11}\ J$.
Answer:
The mass defect of nitrogen - 14 is $0.10851$ amu. The nuclear binding energy of one nitrogen - 14 atom is $1.62\times10^{-11}$ J.